The present invention relates to a demodulator circuit with phase control loop, of the type including a mixer which multiplies, or combines, an input signal with the output signal from a voltage controlled oscillator the control voltage for which is the output voltage from the mixer conducted through a lowpass filter.
A phase locked loop (PLL), or phase control loop is known to be a control system in which the instantaneous phase of a voltage controlled oscillator (VCO) is caused to follow the instantaneous phase of an input signal (broadband PLL) or the phase of the spectral line of the carrier of the input signal (narrow band PLL).
FIG. 1 is a block circuit diagram of a PLL which operates without input signal limitation, that means the amplitude of the input signal is not limited, if the input signal power does not exceed a specified value.
The illustrated circuit includes a mixer M, a voltage controlled oscillator VCO and a lowpass filter TP. A control filter RF with lowpass characteristics is used only for narrow band PLL and is shown in broken lines.
The input signal u.sub.E can be defined as follows: EQU u.sub.E (t)=u.sub.T sin (.omega..sub.T t +.phi.(t)+.phi..sub.T) (1)
where u.sub.T is the input signal carrier peak voltage,
.omega..sub.T is the carrier angular frequency, PA1 .phi.(t) is a time-varying phase which can contain the information to be transmitted. PA1 .phi..sub.T is carrier signal phase. PA1 .omega..sub.os is the VCO output signal residual angular frequency, PA1 .phi..sub.os is the VCO output signal phase,
If u.sub.st is the control voltage of the VCO and k.sub.os its modulation sensitivity, the VCO output signal u.sub.os (t) can de defined as follows: ##EQU1## where u.sub.os is the VCO output signal peak voltage,
.tau. is an integration variable. Its dimension is time.
u.sub.E and u.sub.os are multiplied in mixer M and the result is: ##EQU2## where k.sub.m is the voltage gain of mixer M. With suitable dimensioning of the lowpass filter TP the voltage at the sum frequency is suppressed and the result is: ##EQU3## where k.sub.v is the voltage gain of filter TP.
In a narrowband PLL whose oscillator phase is to be brought only to the spectral line of the carrier of the input signal, the control filter RF filters out all spectral components of u.sub.N except for those at the lowest frequencies and, under the condition that the carrier frequency and the oscillator frequency lie sufficiently closely together, the result is the following: ##EQU4##
This equation can be solved exactly in a manner described in: A. Blanchard, Phase Locked Loops, John Wiley & Sons, New York, 1976, in Chapter 10.1. It is then found that a steady state solution is possible if the following applies; ##EQU5## The following definition therefore applies: ##EQU6## It then follows from (6) that: EQU .vertline..omega..sub.T -.omega..sub.os .vertline.&lt;.omega..sub.P. (8)
.omega..sub.P is a characteristic angular frequency of the loop.
The value of the parameter .omega..sub.p is thus of great significance for the proper operation of the PLL.
When solving equation (5), it is noted that the following asymptotic values appear: ##EQU7##
From the last two equations it becomes evident that the PLL, under condition (8), pulls the oscillator frequency to the carrier frequency of the input signal and establishes a fixed phase relationship between carrier phase and oscillator phase. In other words, the PLL has "settled" on, or tracks, the carrier phase. If the carrier frequency and the oscillator frequency lie sufficiently closely together, the phase shift between u.sub.E and u.sub.os is then almost 90.degree.. The absolute values of the arguments, of the angle functions in equations (4) and (5) must then be much smaller than 1. This enables these equations to be linearized since, for sine functions, the functions can be replaced by their arguments; i.e. if 1.times.1&lt;&lt;1, sin .times..perspectiveto..times.. The result is: ##EQU8## After differentiation with respect to time (t), equation (12) yields the following differential equation ##EQU9##
This is the equation for a lowpass filter with the limit, or half-power cutoff frequency .omega..sub.p /2.pi.. Together with the parameters of the lowpass filter TP and the control filter RF, the parameter .omega..sub.P will thus also influence the stability of the control loop.
A broadband PLL contains no control filter RF. Its work is performed by the lowpass filter TP. For the settled state of operation, differentiation of equation (4) or (11), given that u.sub.st (t) is now identical to u.sub.N (t), respectively, will then produce: ##EQU10##
Here again this is unequivocal lowpass behavior at the limit frequency .omega..sub.P /2.pi., which also influences the stability of the loop. In contradistinction to the narrowband PLL, and if .vertline..phi.(t).vertline. is sufficiently small, the following asymptotic values will appear: ##EQU11## Thus, in contradistinction to the narrowband PLL, in the broadband PLL the momentary phase of the VCO signal adjusts itself to the momentary phase of the input signal and not to its carrier phase. For settling of the broadband PLL, the following restriction must be met instead of (8): EQU .vertline..omega..sub.T -.omega..sub.os .+-..phi.(t).vertline.&lt;.omega..sub.P. (17)
In addition to the demonstrated significance of .omega..sub.P for the settling behavior and the stability of the loop, in the broadband PLL as well as in the narrowband PLL, the value of this parameter usually also has a decisive influence on the further processing of the signals obtained in the PLL. Three examples will be discussed for the purpose of explanation:
It is known that a narrowband PLL can be used as a phase modulation (PM) demodulator if the input signal is modulated with small phase deviations. Due to equations (9) and (10), an oscillator signal will appear in the settled case when the VCO is tuned to the carrier frequency. This oscillator signal is the following: EQU u.sub.os (t)=u.sub.os cos (.omega..sub.T t+.phi..sub.T) (18)
Then it follows, for the voltage u.sub.N (t) at the output of the lowpass filter TP, that: ##EQU12## For values of .vertline..phi.(t).vertline.&lt;&lt;1 it can be stated in approximation that: ##EQU13##
This shows, on the one hand, that the demodulated signal is present at the output of the lowpass filter and, on the other hand, that the amplitude of the output signal depends directly on .omega..sub.P.
It is known that the narrowband PLL can also be used for the synchronous demodulation of an AM signal. FIG. 2 shows the block circuit diagram of such a demodulator.
The amplitude modulated input signal can be shown as follows: ##EQU14## where m(t) is the degree of modulation of the signal carrier, and where .vertline..vertline.m(t).vertline..vertline. means the norm of m(t) being defined as the maximum of the absolute value of m(t).
If the frequencies contained in the sprectrum of m(t) do not fall below a minimum value of f.sub.min &gt;0, a control signal can again be derived, if the control filter RF is of suitable design, as shown in equation (12) which pulls the VCO to the carrier frequency of the input signal and asymptotically sets the VCO phase to the value provided by equation (10). Then the VCO output signal is derived as shown in equation (18) for the settled case and for tuning of the VCO residual frequency to the carrier frequency. After a shift in phase of about 90.degree., this produces the following voltage u.sub.Q (t): EQU u.sub.Q (t)=u.sub.os sin (.omega..sub.T t+.phi..sub.T). (23)
u.sub.Q (t) is combined with u.sub.E,AM in a mixer M2 where the resulting mixer voltage is produced: ##EQU15##
If the lowpass filter TP2 is dimensioned so that signals with frequencies near 2f.sub.T are attenuated to a sufficient extent but signals with frequencies in the low frequency band are practically not attenuated at all, the following voltage appears at the output of TP2: ##EQU16## The gains of mixers M1 and M2 and of the lowpass filter blocks TP1 and TP2 are permanently set. Thus a fixed ratio can be defined as follows: ##EQU17## And it follows that: u.sub.AM (t)=k.sub.AM .omega..sub.P (1+m(t) (27)
At the output of the lowpass filter TP2 there thus is available the demodulated signal with a superposed direct voltage. It is again evident that the amplitude of the output signal depends on the carrier amplitude of the input signal which is a factor of .omega..sub.P.
It is known that FM demodulation can be effected with a broadband PLL. One suitable circuit is that shown in FIG. 1, without the control filter RF. The demodulator output is selected to be the output of the lowpass filter TP, with an output voltage u.sub.N (t).
The input signal is assumed to be as defined in equation (1): EQU u.sub.E (t)=u.sub.T sin (.omega..sub.T t+.phi.(t)+.phi..sub.T). (28)
Then the information to be transmitted is contained in the time derivative of .phi.(t).
In the settled condition, and with tuning of the VCO to the carrier frequency of the input signal, equation (14) provides the following: ##EQU18##
The voltage u.sub.st (t) can thus be considered the output voltage of a lowpass filter which is fed in with the input voltage .phi.(t)/k.sub.os and whose limit frequency is .omega..sub.P /2.pi.. With a sufficiently large value for .omega..sub.P, u.sub.st (t) is therefore=u.sub.N (t), and the demodulated information does not depend on the carrier amplitude of the input signal. Nevertheless the influence of the carrier amplitude is significant, being a factor in the limit frequency .omega..sub.P : if .omega..sub.P /2.pi. becomes less than f.sub.NF,max it must be expected that the information will be greatly distorted.
f.sub.NF,max is the maximum information frequency to be transmitted.
The above examples show the significant influence of .omega..sub.P on a satisfactory result of the circuit function.
The prior art technical solutions counter the dependency of the PLL on the carrier amplitude of the input signal by connecting a limiter bandpass filter ahead of the circuit when angle modulated signals are being processed. The use of a limiter requires the connection of a highly selective filter ahead of the limiter since otherwise the limiter will not perform its amplitude stabilizing function. Due to the extreme nonlinearity of the limiter, there is cause for intermodulation problems. Finally, the limiter worsens the signal to noise ratio within the PLL, as described in: J. C. Springett, and M. K. Simon, "An Analysis of the Phase Coherent-Incoherent Output of the Bandpass Limiter", IEEE Trans. Comm. Techn. Vol. COM-19, No. 1, Feb. 1971, pages 42-49. With amplitude modulated signals, it is known in the prior art to connect an amplifier for automatic gain control ahead of the PLL.
Amplitude regulation ahead of the PLL has already been examined, as described in A. Blanchard, "Phase Locked Loops", John Wiley & Sons, New York, 1976, Chapter 11.2.1; and R. Jaffee, and R. Rechtin, "Design and Performance of Phase Locked Circuits Capable of Near Optimum Performance Over a Wide Range of Input Signal and Noise Levels", IRE Trans. on Inform. Theory, Vol. IT-1, pages 66-76, Mar., 1955.